I think there are two key questions that govern this turn in the conversation:
- Is it better to pursue explicit or implicit knowledge to continue to make gains in strength? (i.e. reading ability or pattern recognition)
- If we assume that implicit knowledge is important, then what is the best way to gain that knowledge?
Most of us agree that both implicit and explicit knowledge are important; we all need a sense of where to play and the reading ability to confirm our intuition. Where we find the appropriate balance is one of the determining factors in our approach to go.
Tsumego can be used to train either reading ability or intuition. When we are first starting out, a lot of the go problems we do are helping us internalize basic shapes so that we can spot the vital point right away. They are training our ability to visualize situations and look ahead on the board at the same time. However, as problem sets grow more complex we often see less repetition of basic shapes and a greater emphasis on pure reading ability. (This is of course not universally true, but the highly lauded Graded Go Problems for Beginners series is a good example of this phenomenon. Book 4 has much less emphasis on recognizing common shapes than previous volumes.) I think this is the point where John suggests a different approach may be needed. (If I've misunderstood, please correct me.)
It's pretty common for folks who get stuck in the SDK range to complain about not knowing where to play once the basic fuseki has been played but a local fight has not yet broken out. We've trained our life and death ability to a reasonable level (again, not universal, and of course we can still improve!) but we miss the forest for the trees. The kind of problem sets that most of us pick up at this level won't help us with that problem. It's tempting to fill in the gaps with explicit knowledge about the direction of play or invading moyos or appropriate reducing moves, but often times the lessons we pick up don't stick because we haven't primed our pattern recognition pumps. In this case, going through a large number of professional games seems like a reasonable way to continue to develop the implicit knowledge that is important at this stage. The benefit is not likely to be limited to strategic notions; we can gain implicit knowledge about key points in fighting the same way. (Note that this is different from the type of study we're doing in the Relentless thread right now, where we are going through one game in detail and trying to explicitly understand what is happening.)
I do think that improvement will require a balance of work on pattern recognition / reading strength, but I don't think that balance
necessarily means doing both equally all the time. In fact, this might be counterproductive. If you want to learn from pattern matching, you may need to immerse yourself in that method for a while. If you want to really improve your reading ability, you may need to focus on nothing else for a time. When we do a little of this and a little of that, it's possible that we're not doing enough of either to be effective. (Note: the above statements are conjecture. I don't have evidence one way or the other.) With this in mind, I think John's advice makes sense for someone who is stuck: immerse yourself in training your pattern recognition ability for a time. Looking at a large number of professional games is probably the best way to do this once you've reached a certain level. If you've given that a sufficient amount of time to be effective and you've stopped seeing improvement, maybe that's a good time to switch to making some of the lessons you picked up explicit or working on your reading ability for a while.
There's a lot of room for individual differences in this approach. If you keep getting stronger by studying fighting technique, have at it! If you keep growing while studying pro games, persist by all means! If mixing your methods of study works, great! We're all likely to have different strengths and weaknesses and different ways of approaching the game, and I doubt there are enough data to make a universal determination about the best approach. But I do think that we tend to get stuck in a rut regarding our approach to study, and trying something novel is a good way to get your brain to reengage with the learning process.
(Haha, as I was writing this Kirby suggested that mixing study types is probably most efficient. I've added a few more "this is conjecture" disclaimers to my original post.

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